Hexagonal bifrustum

The hexagonal bifrustum or truncated hexagonal bipyramid is the fourth in an infinite series of bifrustum polyhedra. It has 12 trapezoid and 2 hexagonal faces. This polyhedron can be constructed by taking a hexagonal dipyramid and truncating the polar axis vertices, making it into two end-to-end frustums.

Hexagonal Bifrustum
Hexagonal bifrustum
TypeBifrustum
Faces12 trapezoids, 2 hexagons
Edges24
Vertices18
Symmetry groupD6h
Dual polyhedronelongated hexagonal dipyramid
Propertiesconvex

Several types of crystal take this shape.[1] It has also been used in the design of 14-sided dice, which may be used to generate randomly chosen playing cards.[2] It also has application in novelty promotional calendars: one month can appear on each of the trapezoids, and an advertising or other message on each of the hexagons.

References

  1. Romanowski, W. (December 1969), "Equilibrium forms of very small metallic crystals", Surface Science, 18 (2): 373–388, doi:10.1016/0039-6028(69)90180-0.
  2. Set of five, fourteen sided poker dice, Patent US 8074986 B1, Douglas A. Gebhart, filed September 30, 2008.
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